Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₇⋊C₈

Direct product G=N×Q with N=C₂³ and Q=C₇⋊C₈

		d	ρ	Label	ID
C₂³×C₇⋊C₈		448		C2^3xC7:C8	448,1233

Semidirect products G=N:Q with N=C₂³ and Q=C₇⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₇⋊C₈) = C₂⁴.Dic₇	φ: C₇⋊C₈/C₁₄ → C₄ ⊆ Aut C₂³	112		C2^3:(C7:C8)	448,82
C₂³⋊₂(C₇⋊C₈) = C₂×C₂₈.₅₅D₄	φ: C₇⋊C₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3:2(C7:C8)	448,740

Non-split extensions G=N.Q with N=C₂³ and Q=C₇⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₇⋊C₈) = C₅₆.D₄	φ: C₇⋊C₈/C₁₄ → C₄ ⊆ Aut C₂³	112	4	C2^3.(C7:C8)	448,110
C₂³.₂(C₇⋊C₈) = C₅₆.₉₁D₄	φ: C₇⋊C₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.2(C7:C8)	448,106
C₂³.₃(C₇⋊C₈) = C₂×C₂₈.C₈	φ: C₇⋊C₈/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.3(C7:C8)	448,631
C₂³.₄(C₇⋊C₈) = C₂²×C₇⋊C₁₆	central extension (φ=1)	448		C2^3.4(C7:C8)	448,630

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